Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

doi:10.1007/s10483-018-2352-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (8): 1119-1146.doi: https://doi.org/10.1007/s10483-018-2352-6

Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

F. E. ÁLVAREZ-BORGES¹, J. BRAVO-CASTILLERO^1,2, M. E. CRUZ³, R. GUINOVART-DÍAZ¹, L. D. PÉREZ-FERNÁNDEZ⁴, R. RODRÍGUEZ-RAMOS¹, F. J. SABINA²

1. Facultad de Matemática y Computación, Departamento de Matemática, Universidad de La Habana, San Lázaro y L, Habana 4, La Habana, CP 10400, Cuba;
2. Departamento de Matemáticas y Mecánica, Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, 01000 CDMX, AP 20-126, México;
3. Departamento de Engenharia Mecânica, Universidade Federal do Rio de Janeiro, Politécnica/COPPE, Caixa Postal 68503, Rio de Janeiro, RJ, CEP 21941-972, Brasil;
4. Departamento de Matemática e Estatística, Universidade Federal de Pelotas, Caixa Postal 354, Pelotas, Rio Grande do Sul, CEP 96010-900, Brasil

收稿日期:2017-07-08 修回日期:2018-03-14 出版日期:2018-08-01 发布日期:2018-08-01
通讯作者: J.BRAVO-CASTILLERO,E-mail:jbravo@matcom.uh.cu E-mail:jbravo@matcom.uh.cu
基金资助:
Project supported by the Desenvolvimento e Aplicações de Métodos Matemáticos de Homogeneização (CAPES) (No. 88881.030424/2013-01), the Homogeneização Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases (CNPq) (Nos. 450892/2016-6 and 303208/2014-7), and the Caracterización de Propiedades Efectivas de Tejidos Biológicos Sanos y Cancerosos (CONACYT) (No. 2016-01-3212)

Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

F. E. ÁLVAREZ-BORGES¹, J. BRAVO-CASTILLERO^1,2, M. E. CRUZ³, R. GUINOVART-DÍAZ¹, L. D. PÉREZ-FERNÁNDEZ⁴, R. RODRÍGUEZ-RAMOS¹, F. J. SABINA²

1. Facultad de Matemática y Computación, Departamento de Matemática, Universidad de La Habana, San Lázaro y L, Habana 4, La Habana, CP 10400, Cuba;
2. Departamento de Matemáticas y Mecánica, Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, 01000 CDMX, AP 20-126, México;
3. Departamento de Engenharia Mecânica, Universidade Federal do Rio de Janeiro, Politécnica/COPPE, Caixa Postal 68503, Rio de Janeiro, RJ, CEP 21941-972, Brasil;
4. Departamento de Matemática e Estatística, Universidade Federal de Pelotas, Caixa Postal 354, Pelotas, Rio Grande do Sul, CEP 96010-900, Brasil

Received:2017-07-08 Revised:2018-03-14 Online:2018-08-01 Published:2018-08-01
Contact: J.BRAVO-CASTILLERO E-mail:jbravo@matcom.uh.cu
Supported by:
Project supported by the Desenvolvimento e Aplicações de Métodos Matemáticos de Homogeneização (CAPES) (No. 88881.030424/2013-01), the Homogeneização Reiterada Aplicada a Meios Dependentes de Múltiplas Escalas con Contato Imperfeito Entre as Fases (CNPq) (Nos. 450892/2016-6 and 303208/2014-7), and the Caracterización de Propiedades Efectivas de Tejidos Biológicos Sanos y Cancerosos (CONACYT) (No. 2016-01-3212)

摘要/Abstract

摘要：

A family of one-dimensional (1D) elliptic boundary-value problems with periodic and rapidly-oscillating piecewise-smooth coefficients is considered. The coefficients depend on the local or fast variables corresponding to two different structural scales. A finite number of imperfect contact conditions are analyzed at each of the scales. The reiterated homogenization method (RHM) is used to construct a formal asymptotic solution. The homogenized problem, the local problems, and the corresponding effective coefficients are obtained. A variational formulation is derived to obtain an estimate to prove the proximity between the solutions of the original problem and the homogenized problem. Numerical computations are used to illustrate both the convergence of the solutions and the gain of the effective properties of a three-scale heterogeneous 1D laminate with respect to their two-scale counterparts. The theoretical and practical ideas exposed here could be used to mathematically model multidimensional problems involving multiscale composite materials with imperfect contact at the interfaces.

关键词: reiterated homogenization method (RHM), non-Newtonian fluid, surge pressure, tripping, annular space, directional wells, imperfect contact, effective coefficient gain, variational formulation

Abstract:

Key words: non-Newtonian fluid, surge pressure, tripping, annular space, directional wells, effective coefficient gain, imperfect contact, reiterated homogenization method (RHM), variational formulation

中图分类号:

F. E. ÁLVAREZ-BORGES, J. BRAVO-CASTILLERO, M. E. CRUZ, R. GUINOVART-DÍAZ, L. D. PÉREZ-FERNÁNDEZ, R. RODRÍGUEZ-RAMOS, F. J. SABINA. Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1119-1146.

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Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

Reiterated homogenization of a laminate with imperfect contact: gain-enhancement of effective properties

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